自对偶麦克斯韦场从克利福德分析

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2024-12-11 DOI:10.1007/s00006-024-01368-1

C. J. Robson

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引用次数: 0

摘要

复函数的研究是基于对满足柯西-黎曼方程的全纯函数的研究。相对较新的Clifford Analysis领域让我们将复杂分析的许多结果扩展到更高的维度。本文利用几何代数的形式将一般Clifford代数的Cauchy-Riemann方程分解为级数，并证明了对于时空代数Cl(3,1)，这些方程是自对偶源自由Maxwell场和无质量不带电荷旋量的方程。这显示了基础物理学和时空的克利福德几何之间的深刻联系。

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Self-Dual Maxwell Fields from Clifford Analysis

The study of complex functions is based around the study of holomorphic functions, satisfying the Cauchy-Riemann equations. The relatively recent field of Clifford Analysis lets us extend many results from Complex Analysis to higher dimensions. In this paper, I decompose the Cauchy-Riemann equations for a general Clifford algebra into grades using the Geometric Algebra formalism, and show that for the Spacetime Algebra Cl(3, 1) these equations are the equations for a self-dual source free Maxwell field, and for a massless uncharged Spinor. This shows a deep link between fundamental physics and the Clifford geometry of Spacetime.

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来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.